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Year 10 Maths Revision: Spring Term For your Autumn Term assessment, you will be doing two GCSE papers:
Paper 1 (80 marks, 1.5 hours): non-calculator
Paper 2 (80 marks, 1.5 hours): calculator
The papers can include any topic you have learnt since the beginning of year 7, so plan your
revision carefully. They will also include topics you haven’t studied yet, as they are full GCSE
papers – be prepared to skip questions you don’t understand.
Unlike other subjects, topics can come up on any paper – both papers are general. In your
final GCSE (and at the end of year 10) you will sit three papers: one non-calculator and two
calculator papers.
In addition to specific revision given to you by your teacher you should do the following:
1. Complete the practice papers you are given; do a few pages a day.
2. Identify questions that you recognise (you think you’ve been taught them) but aren’t
confident to answer.
3. Search for the topic on Hegarty Maths or in your revision guide. Watch the video or
read the explanation, do the questions that go with this, then then try the questions
from the paper again.
4. Revise any other topics you are not confident on, using Hegarty Maths or your revision
guide. Focus in particular on topics you have been taught in year 9 or 10. It’s important
that your revision always includes answering questions.
Below is a list of topics you will have covered in year 10 by the time of your assessment (if
you are in set 1 or 2 you will also have studied additional topics). Make sure you have revised
any of the topics below that you are not confident about.
Ordering decimal numbers
Rounding to decimal places and significant figures; estimation
Fractions and four operations (+, -,×,÷)
Fractions, decimals and percentages
Calculating percentages, simple interest, and repeated percentage change (e.g.
compound interest)
Standard form and four operations (+, -,×,÷)
Laws of indices
Linear and quadratic sequences
Ratio
Pythagoras Theorem
Similarity & enlargement
Bearings
Trigonometry
Algebra: simplifying, expanding, solving, substitution and graphs
Angles: angle rules, angles in parallel lines, angles in polygons
Vectors
GCSE Mathematics
Practice Tests: Set 2
Paper 1F (Non-calculator) Time: 1 hour 30 minutes
You should have: Ruler graduated in centimetres and millimetres,
protractor, pair of compasses, pen, HB pencil, eraser.
Instructions
Use black ink or ball-point pen.
Fill in the boxes at the top of this page with your name, centre number and candidate number.
Answer all questions.
Answer the questions in the spaces provided – there may be more space than you need.
Calculators must not be used.
Diagrams are NOT accurately drawn, unless otherwise indicated.
You must show all your working out.
Information
The total mark for this paper is 80
The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
Keep an eye on the time.
Try to answer every question.
Check your answers if you have time at the end.
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. Change 7800 grams into kilograms.
…………………kilograms
(Total 1 mark)
___________________________________________________________________________
2. Write 0.07 as a percentage
…………………%
(Total 1 mark)
___________________________________________________________________________
3. Write 7.8365 correct to 2 decimal places.
…………………
(Total 1 mark)
___________________________________________________________________________
4. Work out (−5)2
…………………
(Total 1 mark)
___________________________________________________________________________
5. Here is a Venn diagram.
(a) Write down all the numbers in set A.
............................................................................................
(2)
(b) Write down the numbers that are in set A ∩ B.
............................................................................................
(1)
(Total 3 marks)
___________________________________________________________________________
6. Here are four digits.
8 2 4 3
(a) (i) Use two of these digits to make the smallest possible two-digit number.
..........................................
(ii) Use three of these digits to make the three-digit number closest to 300.
..........................................
(2)
Here are four different digits.
5 1 7 9
(b) (i) Put one digit in each box to make the largest total.
You may only use each digit once.
+
(ii) Write down the total.
..........................................
(2)
(Total 4 marks)
___________________________________________________________________________
7.
(a) Write down the coordinates of point A.
(........................... , ...........................)
(1)
(b) On the grid, mark with a cross (×) the point (–3, 0).
Label this point B.
(1)
(Total 2 marks)
___________________________________________________________________________
8. Here are some patterns made from squares.
(a) The diagram below shows part of Pattern number 4
Complete the diagram for Pattern number 4
(1)
(b) Complete the table.
Pattern number 1 2 3 4 5
Number of squares 5 9 13
(1)
(c) Find the number of squares used for Pattern number 10
..................................
(1)
(Total 3 marks)
___________________________________________________________________________
9. Two numbers are added together.
The answer is 15
Both the numbers are factors of 24
What are the two numbers?
.............................................. and ..............................................
(Total 2 marks)
___________________________________________________________________________
10. Make an accurate drawing of an equilateral triangle of side length 5 cm.
(Total 2 marks)
___________________________________________________________________________
11. Here are three calculations.
Which of these calculations has the biggest answer?
You must show how you got your answer.
(Total 3 marks)
___________________________________________________________________________
12. Here is a bus timetable from a Park and Ride car park to a town centre.
Car park Town centre
07 40 07 52
08 00 08 12
08 15 08 27
then every 15 minutes until
18 15 18 27
Sadia gets to the car park at 07 45.
She catches the next bus to the town centre.
(a) What time should the bus get to the town centre?
..............................
(1)
Here is the bus timetable from the town centre to the car park.
Town centre Car park
08 03 08 15
08 35 08 47
09 02 09 14
09 20 09 32
then every 15 minutes until
19 20 19 32
(b) How many buses go from the town centre to the car park between 08 00 and 10 00?
..............................
(2)
Paul wants to leave the town centre after 17 30.
He is going to catch a bus to the car park.
(c) What is the time of the first bus Paul can catch from the town centre after 17 30?
..............................
(1)
(Total 4 marks)
___________________________________________________________________________
13. A charity made an appeal for money.
The charity put the information shown below on a poster.
Hunger appeal
• £3 will buy 5 meals for one person.
• £100 will buy lunches for 80 school children for 5 days.
£3 will buy 5 meals for one person.
(a) Work out the cost of one of the meals.
Give your answer in pence.
.......................................... p
(2)
£100 will buy lunches for 80 school children for 5 days.
(b) Work out the cost of buying lunch for one school child for one day.
..........................................
(3)
(Total 5 marks)
___________________________________________________________________________
14.
A, B, C and D are points on a straight line.
AD = 20 cm
AB = 8.6 cm
BC = CD
Work out the length of BC.
......................................... cm
(Total 3 marks)
___________________________________________________________________________
15. Meela has a fair 6-sided spinner.
The sides of the spinner are numbered 2, 2, 2, 3, 3, 5.
Meela spins the spinner once.
(a) Which number is the spinner least likely to land on?
..........................................
(1)
(b) From the following list, choose the word that best describes the likelihood that the
spinner will land on 2.
impossible unlikely evens likely certain
..........................................
(1)
(c) Write down the probability that the spinner will land on 3.
..........................................
(2)
(Total 4 marks)
___________________________________________________________________________
16. Tom is going to buy 25 plants to make a hedge.
Here is information about the cost of buying the plants.
Tom wants to buy the 25 plants as cheaply as possible.
Should Tom buy the plants from Kirsty’s Plants or from Hedge World?
You must show all your working.
(Total 5 marks)
___________________________________________________________________________
17. You can use this conversion graph to change between pounds (£) and dollars ($).
(a) Use the conversion graph to change £5 to dollars.
$ ....................................
(1)
Ella has $200 and £800
Her hotel bill is $600
Ella pays the bill with the $200 and some of the pounds.
(b) Use the conversion graph to work out how many pounds she has left.
£ ....................................
(4)
(Total 5 marks)
___________________________________________________________________________
18.
A pack of 9 toilet rolls costs £4.23
A pack of 4 toilet rolls costs £1.96
Which pack gives the better value for money?
You must show all your working.
............................................................
(Total 3 marks)
___________________________________________________________________________
19. Dylan is driving from London to Newcastle.
He will drive a total distance of 240 miles.
Dylan leaves London at 09:30
It takes him 11
2 hours to travel the first 90 miles.
(a) Use this information to estimate the time Dylan will arrive in Newcastle.
You must show how you get your answer.
..............................
(3)
(b) Write down one assumption you made in your answer to part (a).
If your assumption is wrong, how would this affect your answer to part (a)?
………………………………………………....…………………………………………..
..……………………………………………………………………………………………
(1)
(Total 4 marks)
___________________________________________________________________________
20.
Describe fully the single transformation that maps shape P onto shape Q.
......................................................................................................................................................
......................................................................................................................................................
(Total 3 marks)
___________________________________________________________________________
21.
The diagram shows the cross-section of a solid prism.
The length of the prism is 2 m.
The prism is made from metal.
The density of the metal is 8 grams per cm3.
Work out the mass of the prism.
.....................................
(Total 5 marks)
___________________________________________________________________________
22.
(a) On the grid, draw the graph of y = 3x + 5 for values of x from –2 to 3
(3)
(b) Explain why the point (6, 24) does not lie on the line y = 3x + 5
(2)
(Total 5 marks)
___________________________________________________________________________
23. Ramesh throws a biased coin.
The probability that the coin will land on a Head is 0.37
(a) Write down the probability that the coin will land on a Tail.
..............................................
(1)
Ramesh is going to throw the coin 500 times.
(b) Work out an estimate for the number of times that the coin will land on a Head.
..............................................
(2)
(Total 3 marks)
___________________________________________________________________________
24. Arwen buys a car for £4000
The value of the car depreciates by 10% each year.
Work out the value of the car after two years.
£ ...................................
(Total 3 marks)
___________________________________________________________________________
25. Write the following numbers in order of size.
Start with the smallest number.
0.038 × 102 3800 × 10–4 380 0.38 × 10–1
......................................................................................................................................................
(Total 2 marks)
___________________________________________________________________________
26. There are 18 packets of sweets and 12 boxes of sweets in a carton.
The mean number of sweets in all the 30 packets and boxes is 14.
The mean number of sweets in the 18 packets is 10.
Work out the mean number of sweets in the boxes.
.........................................
(Total 3 marks)
TOTAL FOR PAPER IS 80 MARKS
GCSE Mathematics
Practice Tests: Set 2
Paper 2F (Calculator) Time: 1 hour 30 minutes
You should have: Ruler graduated in centimetres and millimetres,
protractor, pair of compasses, pen, HB pencil, eraser, calculator.
Instructions
Use black ink or ball-point pen.
Fill in the boxes at the top of this page with your name, centre number and candidate number.
Answer all questions.
Answer the questions in the spaces provided – there may be more space than you need.
Calculators may be used.
Diagrams are NOT accurately drawn, unless otherwise indicated.
You must show all your working out.
Information
The total mark for this paper is 80
The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
Keep an eye on the time.
Try to answer every question.
Check your answers if you have time at the end.
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. Write 0.013 as a fraction.
...........................
(Total 1 mark)
___________________________________________________________________________
2. Change 6.4 centimetres into millimetres
...........................
(Total 1 mark)
___________________________________________________________________________
3. Here is a cuboid.
How many vertices does the cuboid have?
.......................
(Total 1 mark)
___________________________________________________________________________
4. Find the value of 74
………………
(Total 1 mark)
___________________________________________________________________________
5. Here are some patterns made from triangles.
(a) Complete the table.
Pattern number 1 2 3 4 5
Number of triangles 2 4 6
(1)
(b) How many triangles are needed for Pattern number 12?
..........................................
(1)
Luke says that Pattern number 40 has 82 triangles.
(c) Luke is wrong.
Explain why.
...............................................................................................................................................
...............................................................................................................................................
(1)
(Total 3 marks)
___________________________________________________________________________
6. Janet sends parcels by Parcel Express.
The table shows information about the cost of sending a parcel by Parcel Express.
Parcel Express
Weight range Cost
Less than 2 kg £3.80
2 kg to less than 5 kg £5.99
5 kg to 10 kg £71.4
The table below gives information about the numbers and weights of the parcels Janet sent in
April and in May.
Number of parcels
Weight range April May
Less than 2 kg 23 21
2 kg to less than 5 kg 28 27
5 kg to 10 kg 19 32
Janet could have sent her parcels by Parcels R Go.
The table below shows information about the cost of sending a parcel by Parcels R Go.
Parcels R Go
Weight range Cost
0–15 kg £5.99
Janet thinks that it would have been cheaper to send all her parcels by Parcels R Go.
Is Janet right?
You must show your working.
(Total 5 marks)
___________________________________________________________________________
7. Here is a sketch of the end of a roof of a toy house.
Draw an accurate diagram of the end of the roof.
(Total 2 marks)
___________________________________________________________________________
8. On the probability scale, mark with a cross (×), the probability that
(i) you will have something to drink tomorrow.
Label this cross A.
(ii) a teacher chosen at random was born on a Monday.
Label this cross B.
(iii) a fair 6-sided dice will show an even number when thrown.
Label this cross C.
(Total 3 marks)
___________________________________________________________________________
9. Jason collected some information about the heights of 19 plants.
This information is shown in the stem and leaf diagram.
Find the median.
...................................... mm
(Total 2 marks)
___________________________________________________________________________
10. Some of the land in the Netherlands is used to grow bulbs.
The table shows the percentages of this land used to grow the different types of bulbs.
Type of bulb Hyacinth Tulip Daffodil Lily Other
Percentage 8% 50% 12% x% 7%
(a) Work out the value of x.
x = ................................
(1)
The area of land used to grow bulbs for hyacinths is 1200 hectares.
(b) Work out the area of land used to grow bulbs for daffodils.
...................hectares
(2)
(Total 3 marks)
___________________________________________________________________________
11. Barbara has a tube of sweets.
There are 5 sweets in the tube.
There is one sweet of each of these colours in the tube.
red blue green yellow pink
Barbara takes two sweets at random from the tube.
(a) Write down all the possible combinations of colours she can take.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
(2)
(b) What is the probability that Barbara takes a red sweet and a yellow sweet from the tube?
..............................................
(1)
(Total 3 marks)
___________________________________________________________________________
12. Ali takes his car to a garage.
The car has a 5000 mile service.
It also has an MOT test.
(a) Work out Ali’s total bill.
£ ...............................................
(3)
Ali bought his car for £20 000
The car depreciated by 20% the first year.
The car depreciated by 10% the second year.
(b) Work out the value of the car at the end of the second year.
£ ..............................................
(3)
(Total 6 marks)
___________________________________________________________________________
13.
The diagram shows a prism.
In the space below, sketch the front elevation from the direction marked with an arrow.
(Total 2 marks)
___________________________________________________________________________
14. Becky says,
“When you square a prime number you always get an odd number.”
(a) Write down an example to show that Becky is wrong.
..…………………………………………………………………………………………….
(1)
James says,
“When you cube any negative number you always get a negative number.”
(b) James is right.
Explain why.
...……………………………………………………………………………………………
.……………………………………………………………………………………………..
(2)
(Total 3 marks)
___________________________________________________________________________
15. There are some blue counters, red counters and green counters in a bag.
There are twice as many blue counters in the bag as red counters in the bag.
There are 3 times as many red counters in the bag as green counters in the bag.
For the counters in the bag, write down the ratio of
the number of blue counters to the numbers of red counters to the number of green counters.
…………………………..
(Total 2 marks)
___________________________________________________________________________
16. Lev writes down the following
2 5 7
3 8 11
Without doing the exact calculation, explain why Lev’s answer cannot be correct.
…………………………………………………………………………………………….……
…………………………………………………………………………………………………
(Total 1 mark)
___________________________________________________________________________
17.
ABC is a straight line.
Angle BCD = 38°
The reflex angle BCD = 250°
Work out the size of the angle marked x.
Give reasons for your answer.
(Total 4 marks)
___________________________________________________________________________
18. On the grid, draw the graph of y = 2x – 3 for values of x from –2 to 3
(Total 4 marks)
___________________________________________________________________________
19.
A water container has 19.5 litres of water in it.
A cup holds 210 ml of water.
At most 92 cups can be filled completely from the water container.
Explain why.
You must show all your working.
(Total 3 marks)
___________________________________________________________________________
20. The total cost of 3 apples and 4 pears is £1.84
The total cost of 5 apples and 2 pears is £1.76
Work out the cost of one apple and the cost of one pear.
Cost of one apple ......................................................p
Cost of one pear ......................................................p
(Total 4 marks)
___________________________________________________________________________
21. There are a total of 120 counters in a box.
There are only red counters and blue counters in the box.
There are three times as many red counters as blue counters in the box.
Carl takes 3
1 of the red counters from the box.
Kerry takes 80% of the blue counters from the box.
Work out the ratio of the number of red counters to the number of blue counters now in the
box.
Give your ratio in its simplest form.
....................................................
(Total 5 marks)
___________________________________________________________________________
22. Salome hires a chainsaw from the Saws are Us company.
This graph shows the cost of hiring a chainsaw from Saws are Us for up to 12 days.
(a) Find the cost of hiring the chainsaw for 6 days from Saws are Us.
£ ...............................
(1)
The cost of hiring a chainsaw from Saws are Us is £10 plus a daily rate.
(b) Work out the daily rate.
£ ...............................
(1)
Salome wants to compare the cost of hiring a chainsaw from Saws are Us and from Saws to
You.
Saws to You charge £3 for each day of hire.
Salome hires chainsaws for different periods of time.
She wants to use the cheaper company.
(c) Which of these two companies is the cheaper to hire the chainsaw from?
You must show your working and explain your answer.
..............................................................
(3)
(Total 5 marks)
___________________________________________________________________________
23. A square has sides of length 8.4 cm.
Work out the length of a diagonal of the square.
Give your answer correct to 3 significant figures.
.............................................. cm
(Total 3 marks)
___________________________________________________________________________
24. The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
............................ m2
(Total 3 marks)
___________________________________________________________________________
25. Here is a right-angled triangle.
Work out the size of the angle marked x.
Give your answer to the nearest degree.
...............................................................°
(Total 3 marks)
___________________________________________________________________________
26. A box is on a table.
The area of the box in contact with the table is 1500 cm2.
The pressure on the table is 28 newtons/m2.
Work out the force exerted by the box on the table.
........................newtons
(Total 3 marks)
___________________________________________________________________________
Fp
A
p = pressure
F = force
A = area
27. Kelvin and Mamady are in the same class.
The probability that Kelvin arrives on time is 0.7.
The probability that Mamady arrives on time is 0.9.
Complete the probability tree diagram.
(2)
(b) Work out the probability that Kelvin and Mamady both arrive on time.
…………………………
(2)
(Total 4 marks)
TOTAL FOR PAPER IS 80 MARK
